Question: Solve for $x$ and $y$ using elimination. ${2x+4y = 28}$ ${-2x+3y = 7}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $2x$ and $-2x$ cancel out. $7y = 35$ $\dfrac{7y}{{7}} = \dfrac{35}{{7}}$ ${y = 5}$ Now that you know ${y = 5}$ , plug it back into $\thinspace {2x+4y = 28}\thinspace$ to find $x$ ${2x + 4}{(5)}{= 28}$ $2x+20 = 28$ $2x+20{-20} = 28{-20}$ $2x = 8$ $\dfrac{2x}{{2}} = \dfrac{8}{{2}}$ ${x = 4}$ You can also plug ${y = 5}$ into $\thinspace {-2x+3y = 7}\thinspace$ and get the same answer for $x$ : ${-2x + 3}{(5)}{= 7}$ ${x = 4}$